Let's begin by laying out all the reasons why this is not a good idea. First off, a depth guy should have some defensive value. While Abreu wouldn't be as painful to watch as Rivera, he certainly wouldn't provide positive value in the OF, and he can't play CF.
"A DH should have power!" Well, obviously that's not true. No position needs to have power. Power is the most overrated tool in the game. OBP is roughly 1.8 times as valuable as SLG.
"He's old!" Yes, he is, but he's not showing old player skills yet, and the skills that make him so valuable are likely to remain.
Ok, Abreu's days of hitting 20-30 home runs, and stealing 30-40 bases, are long over. 15/15 is probably the most even I would hope for. But what he has done throughout his career, is get on base almost 40% of the time he's stepped up to the plate. Because of that, he's probably going to wind up a HoFer.
Since we're almost certainly going to make the wrong decision and bat Bautista/Encarnacion 3/4, we'll continue to have a hole at the top of the line-up. Lawrie is fast, agressive, and exciting. He'll probably bat lead off, but since he's more of a contact hitter with average power, he really is better off batting second. Still, we'll make the wrong decision and bat him first.
That leaves a glaring hole in the #2 spot. We've filled it with the potent bats of Rasmus, Johnson, and Escobar, without much success. The thing you DON'T need batting in front of Bautista is a home run. You also don't need contact that displays any sort of power (double, triple) because that just ENCOURAGES pitching around Bautista. What you need, is a guy who will take a walk, or do whatever it takes to get on first base, and make the pither take a mental hit if he decides to walk Bautista.
That player, is Bobby Abreu
. Platoon? No need. Abreu has hit lefties better than league average over his career, and hit righties at a hall of fame pace. While his bat is declining, an OBP over .335 vs LHP is a very safe bet, as is an OBP over .350 vs RHP. To me, that's EXACTLY the guy you want in front of Bautista.
The price? 2 million or less I'd guess. He's certainly not a long term solution, and he very well could retire. If he doesn't though, this guy brings patience to a part of our order that desperately needs it, and would add a dimension to our offense that would capitalize on the patience and power that Jose and E5 have.